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Simplifying x2 + 2x + -476 = 0 Reorder the terms: -476 + 2x + x2 = 0 Solving -476 + 2x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '476' to each side of the equation. -476 + 2x + 476 + x2 = 0 + 476 Reorder the terms: -476 + 476 + 2x + x2 = 0 + 476 Combine like terms: -476 + 476 = 0 0 + 2x + x2 = 0 + 476 2x + x2 = 0 + 476 Combine like terms: 0 + 476 = 476 2x + x2 = 476 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 476 + 1 Reorder the terms: 1 + 2x + x2 = 476 + 1 Combine like terms: 476 + 1 = 477 1 + 2x + x2 = 477 Factor a perfect square on the left side: (x + 1)(x + 1) = 477 Calculate the square root of the right side: 21.840329668 Break this problem into two subproblems by setting (x + 1) equal to 21.840329668 and -21.840329668.Subproblem 1
x + 1 = 21.840329668 Simplifying x + 1 = 21.840329668 Reorder the terms: 1 + x = 21.840329668 Solving 1 + x = 21.840329668 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 21.840329668 + -1 Combine like terms: 1 + -1 = 0 0 + x = 21.840329668 + -1 x = 21.840329668 + -1 Combine like terms: 21.840329668 + -1 = 20.840329668 x = 20.840329668 Simplifying x = 20.840329668Subproblem 2
x + 1 = -21.840329668 Simplifying x + 1 = -21.840329668 Reorder the terms: 1 + x = -21.840329668 Solving 1 + x = -21.840329668 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -21.840329668 + -1 Combine like terms: 1 + -1 = 0 0 + x = -21.840329668 + -1 x = -21.840329668 + -1 Combine like terms: -21.840329668 + -1 = -22.840329668 x = -22.840329668 Simplifying x = -22.840329668Solution
The solution to the problem is based on the solutions from the subproblems. x = {20.840329668, -22.840329668}
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